期刊
ALGEBRAS AND REPRESENTATION THEORY
卷 21, 期 5, 页码 1023-1036出版社
SPRINGER
DOI: 10.1007/s10468-018-9810-8
关键词
Orbit method; Corwin-Greenleaf multiplicity function; Multiplicity-free representations; Highest weight representations; Bounded symmetric domains; Branching law; Coadjoint orbit; Geometric quantization
类别
资金
- Japan Society for the Promotion of Science [18H03669]
- Grants-in-Aid for Scientific Research [18H03669] Funding Source: KAKEN
Consider the restriction of an irreducible unitary representation p of a Lie group G to its subgroup H. Kirillov's revolutionary idea on the orbit method suggests that the multiplicity of an irreducible H-module. occurring in the restriction p| H could be read from the coadjoint action of H on OG n pr -1(OH), provided p and. are ` geometric quantizations' of a G-coadjoint orbit OG and an H-coadjoint orbit OH, respectively, where pr : v -1g *. v -1h * is the projection dual to the inclusion h. g of Lie algebras. Such results were previously established by Kirillov, Corwin and Greenleaf for nilpotent Lie groups. In this article, we highlight specific elliptic orbits OG of a semisimple Lie group G corresponding to highest weight modules of scalar type. We prove that the CorwinGreenleaf number (OG n pr -1(OH))/ H is either zero or one for any H-coadjoint orbit OH, whenever (G, H) is a symmetric pair of holomorphic type. Furthermore, we determine the coadjoint orbits OH with nonzero Corwin-Greenleaf number. Our results coincide with the prediction of the orbit philosophy, and can be seen as ` classical limits' of the multiplicity-free branching laws of holomorphic discrete series representations (Kobayashi [ Progr. Math. 2007]).
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据